Exceeds expectations in exhibiting professionalism in accordance with KSDs

Knowledge of Number and Operation: Candidates demonstrate computational proficiency, including a conceptual understanding of numbers, ways of representing number, relationships among number and number systems, and the meaning of operations. (NCTM 9)

Candidate does not demonstrate the ability to: analyze and explain the mathematics that underlies the procedures used for operations involving integers, rational, real, and complex numbers; use properties involving number and operations, mental computation, and computational estimation; provide equivalent representations of fractions, decimals, and percents; create, solve, and apply proportions; apply the fundamental ideas of number theory; make sense of large and small numbers and use scientific notation; compare and contrast properties of number and number systems; represent, use, and apply complex numbers; recognize matrices and vectors as systems that have some of the properties of the real number system; or demonstrate knowledge of the historical development of number and number systems including contributions from diverse cultures.

Candidate demonstrate the ability to: analyze and explain the mathematics that underlies the procedures used for operations involving integers, rational, real, and complex numbers; use properties involving number and operations, mental computation, and computational estimation; provide equivalent representations of fractions, decimals, and percents; create, solve, and apply proportions; apply the fundamental ideas of number theory; make sense of large and small numbers and use scientific notation; compare and contrast properties of number and number systems; represent, use, and apply complex numbers; recognize matrices and vectors as systems that have some of the properties of the real number system; and demonstrate knowledge of the historical development of number and number systems including contributions from diverse cultures.

Candidate demonstrate, beyond expectation, the ability to: analyze and explain the mathematics that underlies the procedures used for operations involving integers, rational, real, and complex numbers; use properties involving number and operations, mental computation, and computational estimation; provide equivalent representations of fractions, decimals, and percents; create, solve, and apply proportions; apply the fundamental ideas of number theory; make sense of large and small numbers and use scientific notation; compare and contrast properties of number and number systems; represent, use, and apply complex numbers; recognize matrices and vectors as systems that have some of the properties of the real number system; and demonstrate knowledge of the historical development of number and number systems including contributions from diverse cultures.

Knowledge of Different Perspectives on Algebra: Candidates emphasize relationships among quantities including functions, ways of representing mathematical relationships, and the analysis of change. (NCTM 10)

Candidate does not demonstrate the ability to: analyze patterns, relations, and functions of one and two variables; apply fundamental ideas of linear algebra; apply the major concepts of abstract algebra to justify algebraic operations and formally analyze algebraic structures; use mathematical models to represent and understand quantitative relationships; use technological tools to explore algebraic ideas and representations of information and in solving problems; or demonstrate knowledge of the historical development of algebra including contributions from diverse cultures.

Candidate demonstrates the ability to: analyze patterns, relations, and functions of one and two variables; apply fundamental ideas of linear algebra; apply the major concepts of abstract algebra to justify algebraic operations and formally analyze algebraic structures; use mathematical models to represent and understand quantitative relationships; use technological tools to explore algebraic ideas and representations of information and in solving problems; and demonstrate knowledge of the historical development of algebra including contributions from diverse cultures.

Candidate demonstrates, beyond expectation, the ability to: analyze patterns, relations, and functions of one and two variables; apply fundamental ideas of linear algebra; apply the major concepts of abstract algebra to justify algebraic operations and formally analyze algebraic structures; use mathematical models to represent and understand quantitative relationships; use technological tools to explore algebraic ideas and representations of information and in solving problems; and demonstrate knowledge of the historical development of algebra including contributions from diverse cultures.

Knowledge of Geometries: Candidates use spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties. (NCTM 11)

Candidate does not demonstrate the ability to: demonstrate knowledge of core concepts and principles of Euclidean and non-Euclidean geometries in two and three dimensions for both formal and informal perspectives; exhibit knowledge of the role of axiomatic systems and proofs in geometry; analyze characteristics and relationships of geometric shapes and structures; build and manipulate representations of two- and three- dimensional objects and visualize objects from different perspectives; specify locations and describe spatial relationships using coordinate geometry, vectors, and other representational systems; apply transformations and use symmetry, similarity, and congruence to analyze mathematical situations; use concrete models, drawings, and dynamic geometric software to explore geometric ideas and their applications in real-world contexts; or demonstrate knowledge of the historical development of Euclidean and non-Euclidean geometries including contributions from diverse cultures.

Candidate demonstrates the ability to: demonstrate knowledge of core concepts and principles of Euclidean and non-Euclidean geometries in two and three dimensions for both formal and informal perspectives; exhibit knowledge of the role of axiomatic systems and proofs in geometry; analyze characteristics and relationships of geometric shapes and structures; build and manipulate representations of two- and three- dimensional objects and visualize objects from different perspectives; specify locations and describe spatial relationships using coordinate geometry, vectors, and other representational systems; apply transformations and use symmetry, similarity, and congruence to analyze mathematical situations; use concrete models, drawings, and dynamic geometric software to explore geometric ideas and their applications in real-world contexts; and demonstrate knowledge of the historical development of Euclidean and non-Euclidean geometries including contributions from diverse cultures.

Candidate demonstrates, beyond expectation, the ability to: demonstrate knowledge of core concepts and principles of Euclidean and non-Euclidean geometries in two and three dimensions for both formal and informal perspectives; exhibit knowledge of the role of axiomatic systems and proofs in geometry; analyze characteristics and relationships of geometric shapes and structures; build and manipulate representations of two- and three- dimensional objects and visualize objects from different perspectives; specify locations and describe spatial relationships using coordinate geometry, vectors, and other representational systems; apply transformations and use symmetry, similarity, and congruence to analyze mathematical situations; use concrete models, drawings, and dynamic geometric software to explore geometric ideas and their applications in real-world contexts; and demonstrate knowledge of the historical development of Euclidean and non-Euclidean geometries including contributions from diverse cultures.

Knowledge of Calculus: Candidates demonstrate a conceptual understanding of limit, continuity, differentiation, and integration and a thorough background in techniques and application of the calculus. (NCTM 12)

Candidate does not demonstrate the ability to: demonstrate a conceptual understanding of and procedural facility with basic calculus concepts; apply concepts of function, geometry, and trigonometry in solving problems involving calculus; use the concepts of calculus and mathematical modeling to represent and solve problems taken from real-world contexts; use technological tools to explore and represent fundamental concepts of calculus; or demonstrate knowledge of the historical development of calculus including contributions from diverse cultures.

Candidate demonstrates the ability to: demonstrate a conceptual understanding of and procedural facility with basic calculus concepts; apply concepts of function, geometry, and trigonometry in solving problems involving calculus; use the concepts of calculus and mathematical modeling to represent and solve problems taken from real-world contexts; use technological tools to explore and represent fundamental concepts of calculus; and demonstrate knowledge of the historical development of calculus including contributions from diverse cultures.

Candidate demonstrates, beyond expectation, the ability to: demonstrate a conceptual understanding of and procedural facility with basic calculus concepts; apply concepts of function, geometry, and trigonometry in solving problems involving calculus; use the concepts of calculus and mathematical modeling to represent and solve problems taken from real-world contexts; use technological tools to explore and represent fundamental concepts of calculus; and demonstrate knowledge of the historical development of calculus including contributions from diverse cultures.

Knowledge of Discrete Mathematics: Candidates apply the fundamental ideas of discrete mathematics in the formulation and solution of problems. (NCTM 13)

Candidates fail to apply the fundamental ideas of discrete mathematics in the formulation and solution of problems. (NCTM 13)

Candidate demonstrates the ability to: demonstrate knowledge of basic elements of discrete mathematics such as graph theory, recurrence relations, finite difference approaches, linear programming, and combinatorics; apply the fundamental ideas of discrete mathematics in the formulation and solution of problems arising from real-world situations; use technological tools to solve problems involving the use of discrete structures and the application of algorithms; and demonstrate knowledge of the historical development of discrete mathematics including contributions from diverse cultures.

Candidate demonstrates, beyond expectation, the ability to: demonstrate knowledge of basic elements of discrete mathematics such as graph theory, recurrence relations, finite difference approaches, linear programming, and combinatorics; apply the fundamental ideas of discrete mathematics in the formulation and solution of problems arising from real-world situations; use technological tools to solve problems involving the use of discrete structures and the application of algorithms; and demonstrate knowledge of the historical development of discrete mathematics including contributions from diverse cultures.

Candidate does not demonstrate the ability to: design investigations, collect data, and use a variety of ways to display data and interpret data representations that may include bivariate date, conditional probability and geometric probability; use appropriate methods such as random sampling or random assignment of treatments to estimate population characteristics, test conjectured relationships among variables, and analyze date; use appropriate statistical methods and technological tools to describe shape and analyze spread and center; use statistical inference to draw conclusions from data; identify misuses of statistics and invalid conclusions from probability; draw conclusions involving uncertainty by using hands-on and computer-based simulation for estimating probabilities and gathering data to make inferences and conclusions; determine and interpret confidence intervals; or demonstrate knowledge of the historical development of statistics and probability including contributions from diverse cultures.

Candidate demonstrates the ability to: design investigations, collect data, and use a variety of ways to display data and interpret data representations that may include bivariate date, conditional probability and geometric probability; use appropriate methods such as random sampling or random assignment of treatments to estimate population characteristics, test conjectured relationships among variables, and analyze date; use appropriate statistical methods and technological tools to describe shape and analyze spread and center; use statistical inference to draw conclusions from data; identify misuses of statistics and invalid conclusions from probability; draw conclusions involving uncertainty by using hands-on and computer-based simulation for estimating probabilities and gathering data to make inferences and conclusions; determine and interpret confidence intervals; and demonstrate knowledge of the historical development of statistics and probability including contributions from diverse cultures

Candidate demonstrates, beyond expectation, the ability to: design investigations, collect data, and use a variety of ways to display data and interpret data representations that may include bivariate date, conditional probability and geometric probability; use appropriate methods such as random sampling or random assignment of treatments to estimate population characteristics, test conjectured relationships among variables, and analyze date; use appropriate statistical methods and technological tools to describe shape and analyze spread and center; use statistical inference to draw conclusions from data; identify misuses of statistics and invalid conclusions from probability; draw conclusions involving uncertainty by using hands-on and computer-based simulation for estimating probabilities and gathering data to make inferences and conclusions; determine and interpret confidence intervals; and demonstrate knowledge of the historical development of statistics and probability including contributions from diverse cultures.

Knowledge of Measurement: Candidates apply and use measurement concepts and tools. (NCTM 15)

Candidate does not demonstrate the ability to: recognize the common representations and uses of measurement and choose tools and units for measuring; apply appropriate techniques, tools, and formulas to determine measurements and their application in a variety of contexts; completes error analysis through determining the reliability of the numbers obtained from measures; or demonstrate knowledge of the historical development of measurement and measurement systems including contributions from diverse cultures.

Candidate demonstrates the ability to: recognize the common representations and uses of measurement and choose tools and units for measuring; apply appropriate techniques, tools, and formulas to determine measurements and their application in a variety of contexts; completes error analysis through determining the reliability of the numbers obtained from measures; and demonstrate knowledge of the historical development of measurement and measurement systems including contributions from diverse cultures.

Candidate demonstrates, beyond expectation, the ability to: recognize the common representations and uses of measurement and choose tools and units for measuring; apply appropriate techniques, tools, and formulas to determine measurements and their application in a variety of contexts; completes error analysis through determining the reliability of the numbers obtained from measures; and demonstrate knowledge of the historical development of measurement and measurement systems including contributions from diverse cultures.